A gun doesn't have to be visible to deter crime. Just the possibility of a victim having a gun is plenty of deterrence. I'd much rather burgle an Australian or English home than one in the US, given how many homes in the US have guns.
This is true. I like people not knowing whether or not I have a gun. It lets me free-ride on other people while greatly reducing the risk of a gun accident in my house.
Yes, but less likely to burgle it while the occupants are at home. Insurance covers stolen possessions, but you can't replace lives lost in a botched burglary or home invasion.